MathDB

line

l

through the point

A

from triangle

ABC

. Point

X

is on line

l

{\omega}_b

and

{\omega}_c

are circles that through points

X,A

and respectively tanget to

AB

adn

AC

. tangets from

B,C

respectively to

{\omega}_b

and

{\omega}_c

meet them in

Y,Z

. Prove that by changing

X

, the circumcircle of the circle

XYZ

passes through two fixed points.
Proposed by Ali Zamani

Problem Statement